Lectures on CFD (Multiphase Flow)

Computational Fluid Dynamics: multiphase flow By: Dr. Alam Nawaz Khan Wardag Department of Chemical Engineering, PIEAS, Islamabad. Email: [email protected] Office: H block

Layout of Lectures • • • •

Classification by Nature of Phases Flow Regime Classification Characteristics of Classes Multiphase Modeling Approaches

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Lectures on Computational Fluid Dynamics: Multiphase Flow

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Classification by Nature of Phases

Gas-Liquid or Liquid-Liquid Flows • Bubbly Flow: discrete gaseous or fluid bubbles in a continuous fluid E.g. : absorbers, aeration, air lift pumps, cavitation, evaporators, flotation, scrubbers

• Droplet Flow: discrete fluid droplets in a continuous gas –E.g. absorbers, atomizers, combustors, cryogenic pumping, dryers, evaporation, gas cooling, scrubbers 7/18/2014 9:02 AM


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• Slug Flow: large bubbles in a continuous fluid –E.g. large bubble motion in pipes or tanks

• Stratified/Free-Surface Flow: immiscible fluids separated by a clearlydefined interface –E.g. sloshing in offshore separator devices, boiling

and condensation in nuclear reactors

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Classification by Nature of Phases • LIQUID-SOLID FLOWS • Slurry Flow: transport of solid particles in liquids. – E.g. slurry transport, mineral processing • Hydrotransport: Densely-distributed solid particles in a continuous liquid – E.g. mineral processing, biomedical and physiochemical fluid systems • Sedimentation: Settling of solid particles in a column of liquid. – E.g. mineral processing 7/18/2014 9:02 AM


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Classification by Nature of Phases • m

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Classification by Nature of Phases • GAS-SOLID FLOWS • Particle-laden Flow: Discrete Solid Particles in a continuous gas. –E.g. cyclone separators, air classifiers, dust collectors, and dust-laden environmental flows

• Pneumatic Transport: Conveying of Solid Particles by gas in Pipelines. –e.g. transport of cement, grains, and metal powders

• Fluidized Beds: Solid Particles suspended in a upward flowing gas. –e.g. fluidized bed reactors, circulating fluidized beds 7/18/2014 9:02 AM


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Classification by Nature of Phases • GELDART CLASSIFICATION

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Classification by Nature of Phases • DRAG FORCE

• The drag coefficient is defined as the ratio of the force on the particle and the fluid dynamic pressure caused by the fluid times the area projected by the particles

Skin Friction

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Skin Friction / Form Drag

Skin Friction / Form Drag


Form Drag

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Classification by Nature of Phases • m

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Classification by Nature of Phases • THREE PHASE FLOWS – Bubbles in a Slurry Flow – Droplets and Particles in Gaseous flow

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Classification by Flow Regimes

Traditional Flow Regime Maps 1. Bubbly 2. Slug 3. Churn 4. Annular

jl = 1 m/s

The Basis is Flow Topology

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Classification by Flow Regimes Gas-Liquid Flow Regimes

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Classification by Flow Regimes

Gas-Liquid Flow Regimes

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Classification by Flow Regimes Gas Solid Flow Regimes

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Classification by Nature of Phases • Two Phase Flow (with phase change)

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Approaches to Multiphase Modeling

• Euler-Lagrange Approach • Euler-Euler Approach – Eulerian Model –Eulerian Granular Phase Model

–Mixture Model –Volume Of Fluid (VOF) Model

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DPM

Euler-Lagrange Approach Discrete Phase Modeling

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Introduction to DPM

• Calculation of the discrete phase trajectory using a Lagrangian formulation that includes • • • •

discrete phase inertia hydrodynamic drag force of gravity both steady and unsteady flows

• Dispersion of particles due to turbulent eddies present in the continuous phase • Heating/cooling of the discrete phase

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Introduction to DPM (contd.) • Vaporization and boiling of liquid droplets • Combusting particles, including volatile evolution and char combustion to simulate • Coal combustion • Optional coupling of the continuous phase flow field prediction to the discrete phase calculations • Droplet breakup and coalescence

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Introduction to DPM (contd.) • Discrete phase α should be very small ( < 10%) • Discrete Phase mass-fraction can be large • The model is appropriate for the modeling of: – spray dryers – coal and liquid fuel combustion

• Inappropriate for: – modeling of liquid-liquid mixtures – fluidized beds – any application where the volume fraction of the second phase is not negligible

• See Fluent user guide for coupling of DPM & other models e.g combustion, reactions etc. 7/18/2014 9:02 AM


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DPM Theoretical Bases • Fluid Phase: – Eulerian formulation as a single phase fluid with or without turbulence.

• Dispersed Phase: – Individual particle motion is traced through particle equation of motion.

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Particle Equations of Motion • Force Balance

– Up = particle velocity – FD = Drag Force

– Fx = Any Other force – Both forces are as Force/particle mass (~acceleration) 7/18/2014 9:02 AM


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Other Forces, Fx • Virtual Mass Force – Force (rate of momentum) required to accelerate the surrounding fluid – Significant for very small particle (dp ~ microns) and when ρ > ρp – Remember – boundary layer around particles are not captured. – Calculated as:

• Pressure gradient force: 7/18/2014 9:02 AM


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Other Forces, Fx

• Thermo-phoretic force • When particle is in fluid with temperature gradient

• DT,p is the thermo-phoretic coefficient, to be provided by user

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Other Forces, Fx

• Or use the Talbot formula for Thermo-phoretic force:

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Other Forces, Fx

• Brownian Force – For very small particles

• Saffman’s Lift force: – This is lift force due to shear (particle in a velocity gradient region)

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Euler-Euler Approach Eulerian (two-fluid) Model

Short Course on “Computational Fluid Dynamics for Industry” at Pakistan Institute of Engineering and Applied Sciences on September 9-10, 2013

Eulerian Model

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Overview

• The Eulerian multiphase model allows multiple separate, yet interacting phases. • The phases can be liquids, gases, or solids in nearly any combination. • An Eulerian treatment is used for each phase • Any number of secondary phases can be modeled (memory is the limit). • For complex multiphase flows, however, you may find that your solution is limited by convergence behavior 7/18/2014 9:02 AM


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Eulerian Model contd.

• A single pressure is shared by all phases. • Momentum and continuity equations are solved for each phase. • Several interphase drag coefficient functions are available, which are appropriate for various types of multiphase regimes. (You can also modify the interphase drag coefficient through user-defined functions, as described in the separate UDF Manual.) • All of the k-e turbulence models are available, and may apply to all phases or to the mixture

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Conservation Equations

Conservation of Mass for Phase q •

A separate mass balance equation is solved for every phase q

•

q is the volume fraction of qth phase

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Conservation Equations

Conservation of Momentum •

A separate momentum balance equation is solved for every phase q

•

q is the qth stress-strain tensor

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Eulerian Model

Limitations • Particle tracking (using the Lagrangian dispersed phase model) interacts only with the primary phase. • Inviscid flow is not allowed. • Melting and solidification are not allowed. • Sharp Interfaces cannot be captured

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Euler- Euler Approach Euler-Granular Phase Model • For dense particulate flows, the DPM cannot be used due to significant volume fraction of solid phase • Solid phase is modeled as a special type of fluid using Kinetic Theory of Gases • This Granular fluid has special correlations for – Granular Pressure – Granular Viscosity – Granular Temperature

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EGPM • Granular Phase modeled as Dense Gas

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EGPM contd. • Viscosity models for Solid phase

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EGPM Governing Equation

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EGPM Governing Equations Contd.

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EGPM Governing Equations Contd. • Various closure relations are used to model the solid phase flow behavior • The three most common are – Gidaspow: good for dense fluidized bed applications. – Syamlal: good for a wide range of applications. – Sinclair: good for dilute and dense pneumatic transport lines and risers.

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EGPM • OpenFOAM simulation of granular flow

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Algebraic Slip (Mixture) Model • Solves one set of momentum equations for the mass averaged velocity and tracks volume fraction of each fluid throughout domain. • Assumes an empirically derived relation for the relative velocity of the phases. • For turbulent flows, single set of turbulence transport equations solved. • This approach works well for flow fields where both phases generally flow in the same direction. 7/18/2014 9:02 AM


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ASM Governing Equations

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ASM Governing Equations contd.

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ASM Governing Equations contd. • Slip Velocity and Drag

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ASM Governing Equations contd. • Limitations

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Volume of Fluid Model • This is an Interface Tracking Method • Other such methods are – Level set method – Moving front method

• Applied to immiscible fluids with clearly defined interface. – Shape of the interface is of interest.

• Typical problems: – Jet breakup. – Motion of large bubbles in a liquid. – Motion of liquid after a dam break.

• Steady or transient tracking of any liquid-gas interface. 7/18/2014 9:02 AM


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VOF contd. • Transient VOF simulation of Liquid Gas interface

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VOF Governing Equations

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VOF Governing Equations contd. • The Volume Fraction equation is solved to track interface

• There are two schemes for interface definition – Piecewise linear scheme – Donor-acceptor scheme 7/18/2014 9:02 AM


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VOF Governing Equations contd.

Actual Interface

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Piecewise Linear Scheme


Donor-Acceptor Scheme

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Porous Media Flow Modeling • There are two main approaches to model single or multiphase flow in Porous media – Microscopic i.e. Pore scale modeling – Macroscopic modeling

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Pore-scale Modeling • This requires resolving of every particle and the interstitial spaces on mesh level • The usual equation for transport phenomena are solved with particles as solid boundaries • Computationally expensive • Find application in research and development of better macroscopic models

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Pore-scale Modeling • CFD simulation of flow at Pore-scale level

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Macroscopic modeling • The Pore-scale modeling approach cannot be used at an industrial scale • Overall flow patterns are more important in practical applications • The porous medium is modeled as a momentum sink in the Navier-Stokes equation • Two type of models exist – Darcian model (for Stoke flow) – Non-Darcian model (for Inertial flow) 7/18/2014 9:02 AM


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Porous Flow Model Governing Equations

• Darcian law for Porous medium – The pressure gradient due to Porous medium is given as

–  is the permeability coefficient for the porous medium –  is the viscosity of fluid

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• Non–Darcian (inertial) flow coefficient • This is given as

– C2 is the inertial pressure loss coefficient

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• The Momentum Sink term including both Darcian and Non-Darcian terms for ith direction is

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• END

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Lectures on CFD (Multiphase Flow)

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